Hex

Hex is a board game played by two players on a hexagonal grid, usually in the shape
of an 11 × 11 rhombus. It was invented
by Piet Hein in 1942 and independently by John Nash in 1948. Hein said that the game occurred to him while contemplating the Four-Color Problem and it soon
became popular in Denmark under the name Polygon. Nash's version
was played by math students at Princeton and a number of other American
campuses.

Players use differently colored pieces – say, red and blue. They take
alternate turns placing a piece of their color inside a hexagon, filling
in that hexagon with their color. Red's goal is to form a red path connecting
the top and bottom sides of the parallelogram; Blue's goal is to form a
path connecting the left and right sides. The game can never end in a tie,
a fact found by Nash: the only way to prevent your opponent from forming
a connecting path is to form a path yourself. When the sides of the grid
are equal, the game favors the first player and the first player has a winning
strategy. There are two ways to make the game fairer. One is to make the
second player's sides closer together, playing on a parallelogram rather
than a rhombus; however, this has been proven to result in a win for the
second player, so it theoretically doesn't improve matters. A better way
is to allow the second player to choose his color after the first player
makes the first move or to make the first three moves, which encourages
the first player to intentionally even out the game.